On A Parabolic Equation in MEMS with An External Pressure

The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the microelectromechanical systems(MEMS) device with an external pressure term. In this paper, we classify the behavior of the solution to this equation. We first show that under certain initial conditions, there exists critical constants $P^*$ and $\lambda_P^*$ such that when $0\leq P\leq P^*$, $0<\lambda\leq \lambda_P^*$, there exists a global solution, while for $0\leq P\leq P^*,\lambda>\lambda_P^*$ or $P>P^*$, the solution quenches in finite time. The estimate of voltage $\lambda_P^*$, quenching time $T$ and pressure term $P^*$ are investigated. The quenching set $\Sigma$ is proved to be a compact subset of $\Omega$ with an additional condition, provided $\Omega\subset R^n$ is a convex bounded set. In particular, if $\Omega$ is radially symmetric, then the origin is the only quenching point. Furthermore, we not only derive the two-side bound estimate for the quenching solution, but also study the asymptotic behavior of the quenching solution in finite time.Comment: 35 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1402.0066 by other author

Convergence to the Grim Reaper for a Curvature Flow with Unbounded Boundary Slopes

We consider a curvature flow $V=H$ in the band domain $\Omega :=[-1,1]\times \R$, where, for a graphic curve $\Gamma_t$, $V$ denotes its normal velocity and $H$ denotes its curvature. If $\Gamma_t$ contacts the two boundaries $\partial_\pm \Omega$ of $\Omega$ with constant slopes, in 1993, Altschular and Wu \cite{AW1} proved that $\Gamma_t$ converges to a {\it grim reaper} contacting $\partial_\pm \Omega$ with the same prescribed slopes. In this paper we consider the case where $\Gamma_t$ contacts $\partial_\pm \Omega$ with slopes equaling to $\pm 1$ times of its height. When the curve moves to infinity, the global gradient estimate is impossible due to the unbounded boundary slopes. We first consider a special symmetric curve and derive its uniform interior gradient estimates by using the zero number argument, and then use these estimates to present uniform interior gradient estimates for general non-symmetric curves, which lead to the convergence of the curve in $C^{2,1}_{loc} ((-1,1)\times \R)$ topology to the {\it grim reaper} with span $(-1,1)$

A Mean Curvature Flow Propagating in a Cylinder at Exponential Speed

In this paper, we study the long time behaviour of mean curvature flow in a cylinder with Robin boundary conditions. Such a boundary condition can force the solution to have a singular behaviour at the boundary when $t\to \infty$. The planar version of this problem has been investigated in an existing literature, where the curve shortening flow in $2$-dimensional band with Robin boundary conditions is shown to converge to a translating Grim Reaper with finite speed and fixed profile. By considering a radially symmetric mean curvature flow, denoted by $u(|x|,t)$, in $(N+1)$-dimensional cylinder ($N\geq 2$), we find in the present paper a new feature of the flow: both the interior gradients and the propagating speed of the flow increase to infinity exponentially, $Du/u\sim x$ and $u\sim C_0 e^{(N-1)t}e^{\frac{|x|^2}{2}}$ as $t\to \infty$ for some $C_0>0$, which is completely different from the 2-dimensional case

Global dynamics of a parabolic type equation arising from the curvature flow

This paper studies a type of degenerate parabolic problem with nonlocal term \begin{equation*} \begin{cases} u_t=u^p(u_{xx}+u-\bar{u}) & 0<t<T_{{\max}},\ 0<x<a, u_x(0,t)=u_x(a,t)=0 & 0<t<T_{{\max}}, u(x,0)=u_0(x) & 0<x<a, \end{cases} \end{equation*} where $p>1$, $a>0$. In this paper, the classification of the finite-time blowup/global existence phenomena based on the associated energy functional and explicit expression of all nonnegative steady states are demonstrated. Moreover, we combine the applications of Lojasiewicz-Simon inequality and energy estimates to derive that any bounded solution with positive initial data converges to some steady state as $t\rightarrow +\infty$

Suppression of long non-coding RNA H19 inhibits proliferation, cell migration and invasion in human cervical cancer cells

Purpose: To determine the expression profile of lncRNA H19 in different cervical cancers, and to decipher its function in the growth and metastasis of cervical cancer.Methods: The analysis LncRNA H19 expression was performed using quantitative real timepolymerase chain reaction (qRT-PCR). Cell counting kit 8 (CCK8) assay was used to assess the viability of the cells. The cells were transfected with Si-H19 using Lipofectamine 2000 and the metastasis of cells was determined by cell migration and invasion assay. Immunoblotting was used to evaluate the protein expression.Results: The lncRNA H19 expression was considerably enhanced in cervical cancer cells, and was about 2.6 to 5.3 times more in cervical cancer cells relative to non-cancer cells. Inhibition of lncRNA caused significant reduction in cervical cancer cell growth in a time-dependent manner. In addition while silencing of lncRNA inhibited the metastasis of HeLa cells. Cell migration and invasion was about 26 % in Si-H19 transfected cervical cancer cells, relative to 65 % in Si-NC cervical HeLa cells. Similarly, cell invasion was 45 % in Si-H19 cervical HeLa cells relative to the negative control (Si-NC). Inhibition of HeLa cell metastasis was also concomitant with decline of metalloproteinases (MMP)-2 and 9expression.Conclusion: lncRNA regulates the growth and metastasis of cervical cancer cells. Thus, IncRNA may be an important therapeutic agent for cervical cancer.Keywords: Cervical cancer, lncRNA, Proliferation, Invasio

Insights into the metabolic profiling of Polygonati Rhizoma fermented by Lactiplantibacillus plantarum under aerobic and anaerobic conditions using a UHPLC-QE-MS/MS system

IntroductionPolygonati Rhizoma is a multi-purpose food with medicinal uses. Fermentation of Polygonati Rhizoma by lactic acid bacteria could provide new insights into the development of Polygonati Rhizoma products.MethodsIn this study, Lactiplantibacillus plantarum was fermented with Polygonati Rhizoma extracts in a bioreactor under aerobic and anaerobic conditions with pH and DO real-time detection. Metabolic profiling was determined by UHPLC-QE-MS/MS system. Principal component analysis and orthogonal partial least-squares discriminant analysis were used to perform multivariate analysis.ResultsA total of 98 differential metabolites were identified in broth after fermentation, and 36 were identified between fermentation under aerobic and anaerobic conditions. The main metabolic pathways in the fermentation process are ABC transport and amino acid biosynthesis. Most of the compounds such as L-arginine, L-aspartic acid, leucine, L-lysine, citrate, inosine, carnitine, betaine, and thiamine were significantly increased during fermentation, playing a role in enhancing food flavor. Compared with anaerobic fermentation, aerobic conditions led to a significant rise in the levels of some compounds such as valine, isoleucine, and glutamate; this increase was mainly related to branched-chain amino acid transaminase, isocitrate dehydrogenase, and glutamate dehydrogenase.DiscussionAerobic fermentation is more beneficial for the fermentation of Polygonati Rhizoma by L. plantarum to produce flavor and functional substances. This study is the first report on the fermentation of Polygonati Rhizoma by L. plantarum and provides insights that would be applicable in the development of Polygonati Rhizoma fermented products

Enhanced photosensitivity of electro-oxidized epitaxial graphene

International audienceWe report the enhanced photosensitivity of epitaxial graphene (EG) after electrochemical oxidation in nitric acid. The onset of photoconductivity appears at a photon energy of ~1.7 eV while the responsivity reaches 2.5 A/W at a wavelength of 470 nm (blue light, energy 2.64 eV) and further increases to 200 A/W in the UV spectral range (3.5 eV, 350 nm). The observed photoresponse is attributed to the formation of deep traps at the electro-oxidized EG interface, which release charge carriers under illumination and prolong the life time of the photocarriers. Potential applications of electro-oxidized EG in ultraviolet photodetection are discusse

Abnormal brain spontaneous activity in major depressive disorder adolescents with non-suicidal self injury and its changes after sertraline therapy

BackgroundNon-suicidal self-injury (NSSI) commonly occurs among adolescents with major depressive disorder (MDD), causing adverse effects on the physical and mental health of the patients. However, the underlying neurobiological mechanism of NSSI in adolescents with MDD (nsMDDs) remains unclear, and there are still challenges in the treatment. Studies have suggested that sertraline administration could be an effective way for treatment.MethodsTo verify the effectiveness and to explore the neurobiological processes, we treated a group of adolescents with nsMDDs with sertraline in this study. The brain spontaneous activity alteration was then investigated in fifteen unmedicated first-episode adolescent nsMDDs versus twenty-two healthy controls through the resting-state functional magnetic resonance imaging. Besides the baseline scanning for all participants, the nsMDDs group was scanned again after eight weeks of sertraline therapy to examine the changes after treatment.ResultsAt pre-treatment, whole brain analysis of mean amplitude of low-frequency fluctuation (mALFF) was performed to examine the neuronal spontaneous activity alteration, and increased mALFF was found in the superior occipital extending to lingual gyrus in adolescent nsMDDs compared with controls. Meanwhile, decreased mALFF was found in the medial superior frontal in adolescent nsMDDs compared with controls. Compared with the pre-treatment, the nsMDDs group was found to have a trend of, respectively, decreased and increased functional neuronal activity at the two brain areas after treatment through the region of interest analysis. Further, whole brain comparison of mALFF at pre-treatment and post-treatment showed significantly decreased spontaneous activity in the orbital middle frontal and lingual gyrus in adolescent nsMDDs after treatment. Also, depression severity was significantly decreased after treatment.ConclusionThe abnormal functional neuronal activity found at frontal and occipital cortex implied cognitive and affective disturbances in adolescent nsMDDs. The trend of upregulation of frontal neuronal activity and downregulation of occipital neuronal activity after sertraline treatment indicated that the therapy could be effective in regulating the abnormality. Notably, the significantly decreased neuronal activity in the decision related orbital middle frontal and anxiety-depression related lingual gyrus could be suggestive of reduced NSSI in adolescent MDD after therapy

Ginsenoside Rg3 Attenuates Lipopolysaccharide-Induced Acute Lung Injury via MerTK-Dependent Activation of the PI3K/AKT/mTOR Pathway

Acute lung injury (ALI) is a common clinical disease with high morbidity in both humans and animals. Ginsenoside Rg3, a type of traditional Chinese medicine extracted from ginseng, is widely used to cure many inflammation-related diseases. However, the specific molecular mechanism of the effects of ginsenoside Rg3 on inflammation has rarely been reported. Thus, we established a mouse model of lipopolysaccharide (LPS)-induced ALI to investigate the immune protective effects of ginsenoside Rg3 and explore its molecular mechanism. In wild type (WT) mice, we found that ginsenoside Rg3 treatment significantly mitigated pathological damages and reduced myeloperoxidase (MPO) activity as well as the production of pro-inflammatory cytokines tumor necrosis factor-α (TNF-α), interleukin-1β (IL-1β) and interleukin-6 (IL-6); furthermore, the production of anti-inflammatory mediators interleukin-10 (IL-10) and transforming growth factor-β (TGF-β), polarization of M2 macrophages and expression levels of the phosphorylation of phosphatidylinositol 3-hydroxy kinase (PI3K), protein kinase B (PKB, also known as AKT), mammalian target of rapamycin (mTOR) and Mer receptor tyrosine kinase (MerTK) were promoted. However, there were no significant differences with regards to the pathological damage, MPO levels, inflammatory cytokine levels, and protein expression levels of the phosphorylation of PI3K, AKT and mTOR between the LPS treatment group and ginsenoside Rg3 group in MerTK-/- mice. Taken together, the present study demonstrated that ginsenoside Rg3 could attenuate LPS-induced ALI by decreasing the levels of pro-inflammatory mediators and increasing the production of anti-inflammatory cytokines. These processes were mediated through MerTK-dependent activation of its downstream the PI3K/AKT/mTOR pathway. These findings identified a new site of the specific anti-inflammatory mechanism of ginsenoside Rg3